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Question
After deducting commission at `7 1/2`% on first
₹ 50,000 and 5% on balance of sales made by him, an agent remits ₹ 93,750 to his principal. Find the value of goods sold by him.
Solution
Agent earns commission at `7 1/2`% i.e. 7.5% on first ₹ 50,000 sales and on balance, at 5%.
Let total sales be ‘x’.
Commission earned on first ₹ 50,000 at 7.5%
`= 7.5/100 xx 50,000`
= ₹ 3,750
Commission earned on balance at 5%
`= (x - 50,000) xx 5/100`
Total commission earned
= Total sales – Amount remitted
= x – 93,750
∴ `(x - 93,750) = 3,750 + 5/100 xx (x - 50,000)`
∴ `(x - 93,750) xx 100 = 3,750 xx 100 + 5(x - 50,000)`
∴ 100x – 93,75,000 = 3,75,000 + 5x – 2,50,000
∴ 100x – 5x = 1,25,000 + 93,75,000
∴ 95x = 95,00,000
∴ x = `(95,00,000)/95`
∴ x = 1,00,000
∴ The value of goods sold by the agent is
₹ 1,00,000.
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